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Two-level multilevel models focusing on inference and diagnostics
Mini Dissertation (MsC (Mathematical Statistics))--University of Pretoria, 2019.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2026
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| _version_ | 1867613647168077824 |
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| access_status_str | Open Access |
| author2 | Ehlers, René |
| author_browse | Ehlers, René |
| author_facet | Ehlers, René |
| collection | Thesis |
| dc_rights_str_mv | © 2025 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Mini Dissertation (MsC (Mathematical Statistics))--University of Pretoria, 2019. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/110463 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:39:27.772Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/110463 Two-level multilevel models focusing on inference and diagnostics Ehlers, René magagula.zwelakhe@up.ac.za Crafford, G Magagula, Zwelakhe L. UCTD Sustainable Development Goals (SDGs) Multilevel linear model Centering Likelihood ratio test Estimation Model Diagnostics Mini Dissertation (MsC (Mathematical Statistics))--University of Pretoria, 2019. This mini-dissertation is aimed at introducing multilevel analysis and how it can be applied to data with a hierarchical structure. Chapter 1 gives an introduction and background of multilevel modeling. In Chapter 2 we start with the theory of linear mixed models (LMMs), which includes the examples and structures of data sets for multilevel models, the general speci cation of LMMs, the di erent types of LMMs, and the multilevel linear model (MLM) speci cation of an LMM. In Chapter 3 we give the theory of estimation of parameters. Three estimation methods are given, namely the maximum likelihood estimation, the restricted maximum likelihood estimation and the iterative generalized least squares method of estimation. We proceed to illustrate the estimation of parameters in Chapter 4. In this chapter data is simulated from a multilevel model having covariates on both level-1 and level-2 of the MLM. We then explore the e ect that tting di erent models to the simulated data have on the within and between covariance parameter estimates. In Chapter 5 we discuss hypothesis testing and model selection. Data is simulated from a speci c MLM. We assume that the model is unknown and proceed to explain how a model is selected through various hypotheses tests. These tests include likelihood ratio test, the t-test, F-test and z-test. Di erent model t statistics are also introduced in this chapter. In Chapter 6 some of the diagnostic tools for multilevel linear models are discussed. The focus is on residual and in uence diagnostics. These tools are again illustrated on simulated data. Chapter 7 illustrates the analysis of multilevel models by making use of a practical example. In the analysis attention is given to centering of explanatory variables to obtain more interpretable coe cients and also the analysis of certain diagnostics to detect in uential observations in the data. Statistics MsC ((Mathematical Statistics) Unrestricted Faculty of Engineering, Built Environment and Information Technology SDG-04: Quality education SDG-09: Industry, innovation and infrastructure 2026-06-08T09:41:06Z 2026-06-08T09:41:06Z 2019 2018 Mini Dissertation * A2019 http://hdl.handle.net/2263/110463 N/A en © 2025 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Sustainable Development Goals (SDGs) Multilevel linear model Centering Likelihood ratio test Estimation Model Diagnostics Two-level multilevel models focusing on inference and diagnostics |
| title | Two-level multilevel models focusing on inference and diagnostics |
| title_full | Two-level multilevel models focusing on inference and diagnostics |
| title_fullStr | Two-level multilevel models focusing on inference and diagnostics |
| title_full_unstemmed | Two-level multilevel models focusing on inference and diagnostics |
| title_short | Two-level multilevel models focusing on inference and diagnostics |
| title_sort | two level multilevel models focusing on inference and diagnostics |
| topic | UCTD Sustainable Development Goals (SDGs) Multilevel linear model Centering Likelihood ratio test Estimation Model Diagnostics |
| url | http://hdl.handle.net/2263/110463 |